The roof front and back are in the shape of congruent isosceles trapezoids. The two sides are in the shape of congruent isosceles triangles. The shingles used on the roof cover 5.50 square meters per bundle. How many bundles are required to cover the roof?
To find the total area of the roof, we need to find the area of the trapezoids and triangles separately and then add them together.
Let's first find the area of one trapezoid:
The area of a trapezoid is given by the formula: A = (1/2) * (a + b) * h
where a and b are the lengths of the parallel sides and h is the height.
Since the trapezoids are congruent isosceles trapezoids, the two parallel sides are equal in length. Let's denote the length of one of these sides as x. The height is not provided, so we will refer to it as h.
Therefore, the area of one trapezoid is: A_trap = (1/2) * (x + x) * h = x * h
Now, let's find the area of one triangle:
The area of a triangle is given by the formula: A = (1/2) * base * height
Since the triangles are congruent isosceles triangles, the base and height are equal in length. Let's denote the length of the base as y.
Therefore, the area of one triangle is: A_tri = (1/2) * y * y = (1/2) * y^2
Given that the shingles cover 5.50 square meters per bundle, the total area of the roof is 2 * A_trap + 2 * A_tri.
Total area = 2(x * h) + 2((1/2) * y^2)
Total area = 2xh + y^2
Now, you can calculate the total area of the roof and divide it by 5.50 to find out how many bundles of shingles are required.